Submonolayer Epitaxy Without A Critical Nucleus

The nucleation and growth of two--dimensional islands is studied with Monte Carlo simulations of a pair--bond solid--on--solid model of epitaxial growth. The conventional description of this problem in terms of a well--defined critical island size fails because no islands are absolutely stable against single atom detachment by thermal bond breaking. When two--bond scission is negligible, we find that the ratio of the dimer dissociation rate to the rate of adatom capture by dimers uniquely indexes both the island size distribution scaling function and the dependence of the island density on the flux and the substrate temperature. Effective pair-bond model parameters are found that yield excellent quantitative agreement with scaling functions measured for Fe/Fe(001).